Question: A circle has a sector with area $\dfrac{29}{5}\pi$ and central angle $232^\circ$. What is the area of the circle? ${9\pi}$ $\color{#9D38BD}{232^\circ}$ ${\dfrac{29}{5}\pi}$
Solution: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{232^\circ}{360^\circ} = \dfrac{29}{5}\pi \div A_c$ $\dfrac{29}{45} = \dfrac{29}{5}\pi \div A_c$ $A_c \times \dfrac{29}{45} = \dfrac{29}{5}\pi$ $A_c = \dfrac{29}{5}\pi \times \dfrac{45}{29}$ $A_c = 9\pi$